Critical magnetic fields of superconducting aluminum-substituted Ba8Si42Al4 clathrate

Critical magnetic fields of superconducting aluminum-substitutedBa8Si42Al4 clathrate

Yang Li,1,a) Jose Garcia,1 Giovanni Franco,2 Junqiang Lu,2 Kejie Lu,1 Bo Rong,3

Basir Shafiq,1 Ning Chen,4 Yang Liu,4 Lihua Liu,5 Bensheng Song,5 Yuping Wei,5

Shardai S. Johnson,6 Zhiping Luo,6 and Zhaosheng Feng7

1School of Engineering, University of Puerto Rico at Mayaguez, Mayaguez, Puerto Rico 00681-9000,USA2Department of Physics, University of Puerto Rico, Mayaguez, Puerto Rico 00681, USA3Communications Research Centre (CRC), Industry Canada, 3701 Carling Avenue, Box 11490, Station H,Ottawa, Ontario K2H 8S2, Canada4School of Materials Science and Engineering, University of Science and Technology Beijing, Beijing 100083,China5Department of Physics, University of Science and Technology Beijing, Beijing 100083, China6Department of Chemistry and Physics, Fayetteville State University, Fayetteville, North Carolina 28301, USA7Department of Mathematics, University of Texas-Pan American, Edinburg, Texas 78541, USA

(Received 2 April 2015; accepted 14 May 2015; published online 3 June 2015)

In recent years, efforts have been made to explore the superconductivity of clathrates containing

crystalline frameworks of group-IV elements. The superconducting silicon clathrate is unusual in

that the structure is dominated by strong sp3 covalent bonds between silicon atoms, rather than the

metallic bonding that is more typical of traditional superconductors. This paper reports on critical

magnetic fields of superconducting Al-substituted silicon clathrates, which were investigated by

transport, ac susceptibility, and dc magnetization measurements in magnetic fields up to 90 kOe.

For the sample Ba8Si42Al4, the critical magnetic fields were measured to be HC1¼ 40.2 Oe and

HC2¼ 66.4 kOe. The London penetration depth of 4360 A and the coherence length 70 A were

obtained, whereas the estimated Ginzburg–Landau parameter of j¼ 62 revealed that Ba8Si42Al4 is

a strong type-II superconductor. VC 2015 AIP Publishing LLC.

[http://dx.doi.org/10.1063/1.4921702]

I. INTRODUCTION

Clathrate materials are extended Si, Ge, and Sn cage-

like solids with sp3-hybridized networks that encapsulate

guest atoms. A wide variety of electronic and vibrational

properties can be produced in these materials by substitution

upon framework sites or through incorporation of ions in

cage-center positions. The main types of clathrates are

A8(IV)46 such as Ba8Si46 (A—alkali or alkaline-earth metal,

IV—group IV element such as Si, Ge, and Sn). This is the

structural type first synthesized and studied by Cros group.1

However, such clathrates have been overlooked for a long

time due to their complexity in synthesis. The discovery of

relatively high TC superconductivity in alkali-metal-doped

C60 fullerenes has inspired efforts to explore the supercon-

ductivity of group-IV clathrates because of the analogy of

the structure for fullerene and clathrate forming polyhedral

cages.2 In particular, the discovered potential of Ge clath-

rates as thermoelectric materials has stimulated an increased

research in this area.3,4

Superconductivity has been found in several clathrates

containing crystalline frameworks of group-IV elements.5,6

Clathrates are the only known sp3 based superconductors

which are unusual as their structure is dominated by strong

covalent bonds, rather than the more typical metallic bonds

found in traditional superconductors. Therefore, it is crucial

to study clathrate superconductors in order to gain a better

understanding of the origin of the attractive interaction

leading to Cooper pairs and the driving mechanism in sp3

covalent systems. As a precursor research, Caplin group

initially searched for superconductivity in type-I and type-II

Na-Si clathrates; however, these original silicon clathrates

were found not to be superconducting.7 A few years later

the type-I Na-Ba-Si clathrate was prepared and shown to be

superconducting with TC near 4 K.8 Advances in synthesis,

in particular, high-pressure methods, led to the preparation

of Ba8Si46 for which the alkali metals were replaced

completely by Ba.9 This composition achieved a supercon-

ducting TC¼ 8 K. Ba8Si46 prepared with a slight deficit of

Ba was found to have TC as high as 9.0 K,10 which is a high-

water mark for superconducting transition temperatures

among sp3-bonded clathrates. Isotope effect measurements

revealed that superconductivity in Ba8Si46 is of the classic

BCS kind, arising from the electron-phonon interaction.11

The enhanced TC in this compound has been shown to arise

predominantly from very sharp features in the electronic

densities of states associated with the extended sp3-bonded

framework.

As shown in the left inset of Fig. 1, type-I clathrate

Ba8Si46 lattice (space group Pm�3n) is an arrangement of two

small pentagonal dodecahedra (Si20) and six big tetrakaideca-

hedra (Si24) offering eight sites per unit cell for guest Ba

atoms. Atomic substitution can tailor these electronic

a)Author to whom correspondence should be addressed. Electronic mail:

[email protected]

0021-8979/2015/117(21)/213912/5/$30.00 VC 2015 AIP Publishing LLC117, 213912-1

JOURNAL OF APPLIED PHYSICS 117, 213912 (2015)

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properties. Substitutions of Si on the framework and Ba in the

center of the cage can profoundly affect superconductivity.

The substitutional effects of Si framework on superconductiv-

ity for Ba8Si46–xLx with L¼Ga, Al, Ag, Au, Cu, Ge, and Ni

have been studied by several groups.2 Consistent with the lat-

est research findings, these investigations showed a

progressive decrease of the critical temperature with the

increase in the L content "x" depending on the substituting

elements. Likewise, the substitutional effects of guest atoms

in the center of cages have also been investigated in the

Ba8–xGxSi46 (G¼ Sr, Ca, Na, K, and Eu) systems.12–15 In all

these cases, TC was found to decrease with the increase in the

content of substitution atoms, while superconductivity

vanished after a critical substitution level was reached. The

destructive effect on superconductivity generally is attribut-

able to a reduction in density of states at Fermi-level (N(EF)),

and a lowering of the carrier concentration, combined with

the disrupted continuity of the sp3-hybridized framework.16,17

Based on the calculation of the phonon-dispersion relations

and vibrational density of states for Al-doped silicon clath-

rates,18 the high frequency acoustic branch has a red shift

with the doping of Al. The decreased frequency of bond-

stretching vibration modes is another reason for the suppres-

sion of TC induced by Al substitution. In addition, the

substitution of Eu for Ba results in a strong suppression of

superconductivity; Eu-doping largely decreases the supercon-

ducting volume and the transition temperature TC. Eu atoms

enter the clathrate lattice and their magnetic moment breaks

paired electrons.15 However, one of the more important

aspects, namely, the critical magnetic field of clathrate super-

conductors has not been investigated comprehensively. This

report presents a detailed study of superconducting behavior

in the Al-doped Ba8Si46 clathrate compounds, based on elec-

trical resistivity and magnetic susceptibility measurements in

the low-temperature region. The exceptional attention is

devoted to Ba8Si42Al4 clathrate with robust type-II character-

istics. A careful attempt is made in order to ascertain its basic

superconducting properties. Important superconducting

parameters, such as, the critical fields, coherence length,

penetration depth, and Ginzburg-Landau parameter are also

estimated.

II. EXPERIMENTAL METHODS

The synthesis of Ba8Si46�xAlx was performed based on

the multistep melting of Ba, Al, and Si under argon atmos-

phere and subsequent solid-state reaction.19 The samples

were characterized and analyzed by X-ray diffraction and

electron probe microanalyzer (EPMA). Structural refinement

of the powder X-ray diffraction data was carried out using

the GSAS software package.20,21 The samples were analyzed

for resistivity and magnetic susceptibility by a cryogen-free

physical properties measurement system (Cryogenic in

London).

Analysis by powder X-ray diffraction showed character-

istic type-I clathrate reflections for Ba8Si46�xAlx samples.

As shown in Fig. 1, the sample of Ba8Si42Al4 with dilute Al-

doping, exhibited the main phase to be type-I clathrate with

small quantities of impure phases such as silicon and BaSi2(orthorhombic phase). As a result of the refinement, Al was

found to preferentially occupy the 6c framework sites for

dilute doping, however, for heavy substitution, Al inclined

towards a random distribution of the other 16i and 24k sites.

The lattice parameter of Ba8Si42Al4 was calculated as

a¼ 10.39 A. The lattice parameters of Ba8Si46-xAlx exhibited

an increasing trend with x due to the larger atomic size of Al

than that of Si.17

A JEOL 8530F EPMA was used to determine the stoi-

chiometry and grain size of the samples. The samples were

embedded using Buehler Epoxy Resin and Hardner, which

were placed in a Buehler Cast N’ Vac 1000 Vacuum

Impregnation System to suck out the air bubbles in voids to

fill with the epoxy. These embedded samples were then

mechanically polished to provide a flat surface of the crystals

for the microprobe analysis, and coated with a thin carbon

film for the EPMA analysis. Several spots on each crystal

were analyzed for Ba, Al, and Si using a beam current

density approximately 10 nA. EPMA imaging showed main

phase of clathrate and a small amount of impurity phases

such as Si, BaSi2, and SiO2 at grain boundary. The EPMA

composition analysis on clathrate phase showed the average

composition of crystals (Ba8Si38.83Al3.47) to be consistent

with Zintl concept. As an example shown in the right inset of

Fig. 1, the EPMA mapping obviously showed the homogene-

ity in the distribution of the constituent elements in the clath-

rate phase. A little amount of impurity phase, however,

existed in grain boundaries of sample. To characterize the

grain size, EPMA was used on samples. The microstructures

of the sample are with nubbly grains. There is no texture,

and the grains are randomly oriented with porosity. The av-

erage grain sizes were measured by the linear intercept

method; sample has an average grain size �20 lm.

III. RESULTS AND DISCUSSIONS

The temperature dependence of the AC and DC suscepti-

bility measured on Ba8Si42Al4 is shown in Figs. 2(a) and

2(b), respectively. For both AC and DC magnetic measure-

ments, the superconducting onset temperature TC,onset was

FIG. 1. The refined powder XRD pattern of Ba8Si42Al4 sample can be fully

indexed with the type-I clathrate structure. Red, green, and blue ticks mark

the positions of allowed reflections of type-I clathrate, diamond Si, and

BaSi2, respectively. Right inset: an EPMA image. Left inset: type-I clathrate

structure of Ba8Si46.

213912-2 Li et al. J. Appl. Phys. 117, 213912 (2015)

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obtained as 5.7 K. The temperature dependence of the AC

susceptibility was measured in zero static field with ac field

amplitude of 3 Oe at a frequency of 256 Hz. At about 5.7 K,

the sample started to show superconducting characteristics;

the in-phase susceptibility (v0) suddenly dropped and the out-

of-phase susceptibility (v00) peaked.

A superconducting transition in Ba8Si42Al4 was also

observed in dc magnetic susceptibility (vdc¼M/H) measure-

ments. Figure 2(b) shows the zero-field-cooled (ZFC)

warming data and the field-cooled (FC) data for the applied

magnetic Field at H¼ 50 Oe. The magnetization observed in

the superconducting state does not saturate at the lowest tem-

perature measured. The enhancement of the diamagnetism

below the superconducting transition temperature TC origi-

nates from the screening supercurrents (ZFC regime) and the

Meissner effect of magnetic flux expulsion (FC regime). Also,

as shown in Fig. 3, the existence of the hysteresis between the

two magnetization curves for the ZFC and the FC modes indi-

cates that the compound is a type-II superconductor. The

superconducting volume fraction was estimated to be 30%

according to the ZFC susceptibility at T¼ 2 K. On the other

hand, the diamagnetic transition in the FC process is not too

small. This is due to a weak magnetic flux pinning force of

the sample, i.e., the expulsion of the magnetic flux from the

sample by the Meissner effect is large on cooling in the field.

Such a small difference in the magnitude of diamagnetic sus-

ceptibility between ZFC and FC processes is widely observed

for superconductors having weak flux pinning forces.

In addition, FC magnetization values were carried out as

a function of temperature in applied fields from 50 to 5 kOe,

as shown in Fig. 3. Flux expulsion (Meissner effect)

decreases with increasing external field; the magnetic field

easily suppresses the magnitude of superconducting response.

We observed that with applied field increasing, there occurs a

strong reduction in superconducting volume. As shown in the

inset of Fig. 3, the superconducting volume Vsup decreases

with increasing field in a log linear behavior, log Vsup¼ aþ blog H, with a¼ 1.9 and b¼�1.4.

Fig. 4 shows the initial magnetization at low fields. The

magnetization gradually deviates from the perfect diamagne-

tization line. The lower critical field HC1(T) of this supercon-

ductor from the first deviation from linearity in the low-field

regions in the M(H) scans was estimated to be of the order

of HC1(0)¼ 40.2 Oe, as shown in the inset of Fig. 5,

assuming a simple parabolic T dependence in the form of

HC1(T)¼HC1(0)(1� t2) where t¼ T/TC.

The large changes at T¼ 5.7 K in the AC and DC sus-

ceptibility were accompanied by a distinct drop in electrical

resistivity of the Ba8Si42Al4 sample. The four-probe trans-

port measurements also confirmed that Ba8Si42Al4 enters

into a superconducting state at 5.7 K. The sample showed a

metallic behavior in the normal state. The agreement of the

transition temperatures measured by both ac and dc suscepti-

bility as well as resistivity is a clear evidence of bulk super-

conductivity in Ba8Si42Al4.

Temperature dependence of the upper critical field HC2

of Ba8Si42Al4 is shown in Fig. 5. HC2 is estimated based on

the electrical resistivity R(T) and R(H) measurement, respec-

tively. As shown in the right inset of Fig. 5, the R-Hmeasurements were carried out at various fixed temperatures

which were set near and below TC from 2 to 6 K. The sample

FIG. 2. Magnetic susceptibility of Ba8Si42Al4 vs. temperature. (a)

Temperature dependence of the in-phase (v0) and out-of-phase (v00) AC sus-

ceptibility, measured in the zero field, (b) DC magnetization measurement

under the ZFC/FC protocol is shown for an external field of 50 Oe.

FIG. 3. The ZFC magnetization under different fields for Ba8Si42Al4. Inset:

Superconducting volume (Vsup) decreasing with external field according to a

linear log behavior, with the fitted curve log Vsup¼ aþ b log H.

FIG. 4. The magnetization curves at various temperatures from 2 to 5.5 K

for Ba8Si42Al4. The inset shows T dependence of the lower critical field

HC1(T). The dashed line is a fit assuming a parabolic T dependence, giving

HC1 (0)¼ 40.2 Oe.

213912-3 Li et al. J. Appl. Phys. 117, 213912 (2015)

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was warmed up to 20 K before the R-H measurement at each

temperature was taken. Above superconducting transition

temperature, the normal resistance of sample was about 55

mX. The upper critical field HC2 at different temperatures

was obtained from the R-H measurements at the field where

the resistance reached half of the normal-state resistance RN.

The arrow points to the defined upper critical field HC2 at

2 K. The resistance approaches RN gradually because of the

magnetoresistance effect. A broadening of the transition

curves was observed at low temperature, which is caused at

least partially by flux-flow effects at high magnetic fields.

The transition widths gradually broaden from 14.2 kOe at 5 K

to 26.1 kOe at 2 K. The solid square symbols (�) in Fig. 5

show HC2 vs temperature for the Ba8Si42Al4, which were

determined from R(H) curve collected at various fixed tem-

peratures. This HC2 curve shows a perfect linear dependence

on T near TC, which is a typical property of a superconductor

with a high value of the Ginzburg-Landau parameter j.

In addition, the left inset of Figure 5 shows the R(T)

curves of the sample Ba8Si42Al4 at different applied fields. In

the normal state, the sample resistance change is flat from 60

mX at 300 K to 55 mX just above the transition temperature,

which still showed weak metallic temperature dependence

with residual resistivity ratios (RRR) of 1.1 only. Here, the

upper critical field HC2 in R(T) measurement was defined as

the zero resistance temperature limit. The temperature

dependence of HC2 labelled with the solid circle symbol (•) is

plotted in Fig. 5. Using the values of HC2 for zero resistance

TC0, the upper critical field was evaluated to be HC2¼ 66.4

kOe and TC¼ 5.32 K by fitting the data to the generalized

Ginzburg-Landau model: HC2(T)¼HC2(0)(1� t2)/(1þ t2),

where t¼ T/TC. This fitted HC2(0) is below the BCS Pauli

paramagnetic limit (HC2,Pauli¼ 1.83 TC¼ 97.4 kOe). From

the estimates of HC1 and HC2, the penetration depth, k,

and the coherence length, n, were determined using

the Ginzburg–Landau equations:22 l0HC2 ¼ U0

2pn2 and

l0HC1 ¼ U0

4pk2 lnðk=nÞ þ C1Þð , where j¼ k/n is the

Ginzburg–Landau parameter, U0 ¼ p�hc=e is the flux quan-

tum, and C1¼ 0.497.23 From HC1¼ 40.2 Oe and HC2¼ 66.4

kOe, k¼ 4360 A and n¼ 70 A were obtained. Hence, j� 62

was found indicating this material is a strongly type-II super-

conductor. These values can be compared to those obtained

for Ba8Si46 (k� 4000 A, n� 72 A, and j� 56).24 We found

that both materials have the same order of magnitude for kand n. It is evident that in the type IX chiral-structure clath-

rate Ba24Ge100, k� 6500 A and n� 310 A (Ref. 25) are

bigger than the values for Ba8Si40Al4 reported here.

The existence of the superconducting mixed state char-

acterizes Ba8Si42Al4 as a type-II superconductor. Evidence

for a type II superconducting state can be seen as well in Fig.

6 where M-H loop has been plotted for T¼ 2, 3, and 4 K.

Figure 6 shows that the magnetic field dependence of the

magnetization M below TC is irreversible. At these tempera-

tures, the magnetic hysteresis (the width of the M-H loops)

decreases with the applied field, but remains nonzero at 50

kOe below T¼ 4 K.

Because our superconducting Ba8Si42Al4 sample is a

polycrystalline compound, which contains a large array of

grains and grain boundaries through which the current can

flow. Application of a magnetic field to the polycrystalline

sample sets up screening currents both within grains and on

a macroscopic scale. Consequently, the irreversible magnetic

moment Dm is a direct measure of these screening currents,

and can be written as a sum of inter- and intra-granular

contributions

Dm5ð2=3ÞV½KJinter 1 a0Jintra�; (1)

where V is the volume of the superconductor, a0 is the typi-

cal grain size, and K the length scale of coherent current

flow (current carrying length scale).26 Analysis of Dmrequires knowledge of K, which is complicated by the

presence of weak links in polycrystalline superconductors.

With increasing magnetic field and temperature, the weak

FIG. 5. Temperature dependence of the upper critical field HC2 of

Ba8Si42Al4. The solid circle symbols (•) were determined from zero resist-

ance temperature TC0 in the R(T) data, and the dashed line is a fit to the data

using a GL model, giving HC2(0)¼ 66.4 kOe. The solid square symbols (�)

were determined from R(H) curve collected at fixed temperature. Right

inset: R(H) curve at fixed temperature. The black arrow indicates the deter-

mined upper critical field at 2 K. Left inset: the resistance versus temperature

at various fields H from 0 to 90 kOe with an interval 5 kOe. The black arrow

indicates the zero resistance temperature corresponding to the upper critical

field at H¼ 0.

FIG. 6. M-H hysteresis of Ba8Si42Al4 at 2, 3, and 4 K, respectively. Upper

inset: JC-H dependences at 2, 3, and 4 K, respectively. Lower inset: The pin-

ning force FP(¼ jJC�Hj) against magnetic field H.

213912-4 Li et al. J. Appl. Phys. 117, 213912 (2015)

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links tend to fragment the pattern of screening currents, so

that K cannot be equated simply to the sample physical

dimension. However, previous analysis has shown that at

given T and H, the initial “reverse-leg” magnetic susceptibil-

ity is proportional to K, which allows the latter to be

estimated27

ðdDM=dBÞ/ðK=tÞ; (2)

where t is the thickness of the superconductor. A series of

magnetization loops of Ba8Si42Al4 sample at 2 K were also

measured. According to the initial “reverse-leg” magnetic

susceptibility, the current carrying length scale K was

estimated under different applied magnetic fields. The length

scale of coherent current flow rapidly decreased with the

field. When the applied field increases, the dominant mag-

netic screening currents circulate only on a scale correspond-

ing to a grain size (�20 lm). This implies that at high fields

the intergranular current is rather small, and the intragranular

current is dominant. Thus, at high fields Dm becomes

increasingly dominated by the intra-granular term in Eq. (1).

Therefore, only the contribution of intragranular current

needs to be considered, so that the critical current density

JC 5 3Dm/2Va0, where Dm and a0 are the irreversible mag-

netic moment and the average size of grains, respectively,

and V is the sample volume. The JC-H dependence at 2, 3,

and 4 K, respectively, for Ba8Si42Al4 sample is shown in the

upper right inset of Fig. 6. The flux pinning behavior of

Ba8Si42Al4 compound can be inferred from lower right inset

of Fig. 6, which plots the pinning force FP( 5 jJC 3 Hj)against magnetic field. The irreversible magnetic moment

would be caused by defects and finely dispersed impurities

in the grain boundary of the sample; they trap magnetic flux

through the sample, however, such precipitate phases may

not be responsible for the JC increase in intragranular. We

note that at a given temperature, the JC decreases rapidly

with the increasing applied field, especially at higher

temperature, which indicating that the flux pinning is still

rather weak in Ba8Si42Al4. For instance, at 2 K, the JC

decreases from a maximum of 1.7� 106 A/cm2 at H¼ 0 to

4.8� 105 A/cm2 at H¼ 4 kOe. For Ba8Si42Al4 sample, the

field-dependent JC(H) showed that the pinning behavior is

similar to neither high-TC cuprate superconductors nor MgB2

compound. As shown in Fig. 6, there is no JC(H) second

peak and fishtail, which appeared in the Eu1–xYxBa2Cu3Oy.28

On the other hand, the JC(H) of Ba8Si42Al4 does not have a

good field-dependent behavior such as in the MgB2,

especially in the high field regions.29 Clearly, in Ba8Si42Al4compound, there are no structural deficiencies acting as

effective pinning centers, although structural defects induced

by Al-doping into the Si framework result in some flux

pinning.

In conclusion, detailed investigations of the properties

of a superconductor Ba8Si42Al4 clathrate are reported.

Magnetization and transport measurements have been

performed, which showed the Ba8Si42Al4 clathrate is a bulk

superconductor. The upper and lower critical fields are

estimated to be HC1(0)¼ 40.2 Oe and HC2¼ 66.4 kOe,

respectively. The London penetration depth k¼ 4360 A and

the coherence length n¼ 70 A are obtained, while the

Ginzburg–Landau parameter j¼ 62 indicates this material is

a strong type-II superconductor.

ACKNOWLEDGMENTS

This work was supported in part by the National Science

Foundation (DMR-0821284), NASA (NNX10AM80H and

NNX07AO30A). The EPMA work at FSU was supported by

NSF (HRD-1436120) and DoD (W911NF-09-1-0011 and

W911NF-14-1-0060).

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